# Lect12 - Lecture 12, p 1 Lecture 12: Particle in 1D boxes,...

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Unformatted text preview: Lecture 12, p 1 Lecture 12: Particle in 1D boxes, Simple Harmonic Oscillators U U x n=0 n=1 n=2 n=3 U(x) (x) Lecture 11, p 2 Particle in Infinite Square Well Potential U = U = x L E n n=1 n=2 n=3 The discrete E n are known as energy eigenvalues : = = = = 2 2 2 2 2 2 2 1 1 2 1.505 2 2 where 8 n n n n p h eV nm E m m h E E n E mL electron (x) L n=1 n=2 x n=3 ( 29 2 ( ) sin sin sin for n n n n x k x x x x L L = = - + = h 2 2 2 ( ) ( ) ( ) ( ) 2 n n n n d x U x x E x m dx = n 2L n Lecture 12, p 3 An electron is trapped in a quantum wire that is L = 4 nm long. Assume that the potential seen by the electron is approximately that of an infinite square well . 1: Calculate the ground (lowest) state energy of the electron . U= U= x L E n n=1 n=2 n=3 The idea here is that the photon is absorbed by the electron, which gains all of the photons energy (similar to the photoelectric effect). 2: What photon energy is required to excite the trapped electron to the next available energy level ( i.e. , n = 2)? Quantum Wire Example Lecture 12, p 4 Lecture 12, p 5 2. If we decrease the size of the dot, the difference between two energy levels (e.g., between n = 7 and 2) will a) decrease b) increase c) stay the same 1. An electron is in a quantum dot. If we decrease the size of the dot, the ground state energy of the electron will a) decrease b) increase c) stay the same Act 1 U= U= x L E n n=1 n=2 n=3 Lecture 12, p 6 Baseball Example Why dont we worry about quantized energy levels in tha macroscopic world?...
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## This note was uploaded on 02/21/2011 for the course PHYS 214 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lect12 - Lecture 12, p 1 Lecture 12: Particle in 1D boxes,...

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